From df8386f75b0538075d72d52693836bb8878f505b Mon Sep 17 00:00:00 2001
From: KatolaZ <katolaz@yahoo.it>
Date: Mon, 19 Oct 2015 16:23:00 +0100
Subject: First commit of MAMMULT code

---
 models/correlations/fit_utils.c | 382 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 382 insertions(+)
 create mode 100644 models/correlations/fit_utils.c

(limited to 'models/correlations/fit_utils.c')

diff --git a/models/correlations/fit_utils.c b/models/correlations/fit_utils.c
new file mode 100644
index 0000000..e9e3954
--- /dev/null
+++ b/models/correlations/fit_utils.c
@@ -0,0 +1,382 @@
+/**
+ *
+ * Fit a given sequence with a power-law function
+ *
+ * a*x^{b}
+ *
+ * The fit is actually performed as a linear fit on the
+ * exponential-binned log-log distribution
+ *
+ *
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include <gsl/gsl_fit.h>
+
+/**
+ * 
+ * Load a sequence from a file, which contains one element on each line
+ *
+ */
+
+void load_sequence(char *fname, double **v, int *N){
+
+  int size;
+  char buff[256];
+  
+  FILE *f;
+  
+  f = fopen(fname, "r");
+  if (!f){
+    fprintf(stderr, "Error opening file %s!!!! Exiting...\n", fname);
+    exit(1);
+  }
+  
+  *N =0;
+  size = 10;
+  if (*v == NULL)
+    *v = malloc(size * sizeof(double));
+  else{
+    *v = realloc(*v, size * sizeof(double));
+  }
+  
+  while (fgets(buff, 255, f)){
+    (*v)[*N] = atof(buff);
+    *N += 1;
+    if (*N == size){
+      size += 10;
+      *v = realloc(*v, size * sizeof(double));
+    }
+  }
+  *v = realloc(*v, (*N) * sizeof(double));
+  fclose(f);
+}
+
+
+/**
+ *
+ * Load a sequence, getting the "col"-th column of the input file
+ *
+ */
+
+void load_sequence_col(char *fname, double **v, int *N, int col){
+
+  int size, n;
+  char buff[256];
+  char *ptr;
+
+  FILE *f;
+  
+  f = fopen(fname, "r");
+  if (!f){
+    fprintf(stderr, "Error opening file %s!!!! Exiting...\n", fname);
+    exit(1);
+  }
+  
+  *N =0;
+  size = 10;
+  if (*v == NULL)
+    *v = malloc(size * sizeof(double));
+  else{
+    *v = realloc(*v, size * sizeof(double));
+  }
+  
+  while (fgets(buff, 255, f)){
+    ptr = strtok(buff, " ");
+    if (col > 0){
+      n = 0;
+      while (n<col){
+        ptr = strtok(NULL, " ");
+        n += 1;
+      }
+    }
+    (*v)[*N] = atof(ptr);
+    *N += 1;
+
+    if (*N == size){
+      size += 10;
+      *v = realloc(*v, size * sizeof(double));
+    }
+  }
+  *v = realloc(*v, (*N) * sizeof(double));
+  fclose(f);
+}
+
+
+/**
+ *
+ * Make the exponential binning of a distribution, with a giving
+ * exponent alpha. The value of y[i] is the number of elements of v
+ * whose value lies between x[i-1] and x[i]...
+ *
+ */
+
+void exp_bin_cnt(double *v, int N, double alpha, double **x, double **y, int *num){
+  
+  double min_v, max_v, val, last_val;
+  int i, j, size, num_x;
+  double last_size, new_size;
+  
+  min_v = max_v = v[0];
+  
+  for (i=1; i<N; i ++){
+    if (v[i] > max_v)
+      max_v = v[i];
+    else if (v[i] > 0 && v[i] < min_v)
+      min_v = v[i];
+  }
+
+  size = 10;
+  if (*x == NULL){
+    *x = malloc(size * sizeof(double));
+  }
+  else{
+    *x = realloc(*x, size * sizeof(double));
+  }
+  
+  val = min_v;
+  last_size = min_v;
+  (*x)[0] = min_v;
+  num_x = 1;
+
+  while(val < max_v){
+    new_size = last_size * alpha;
+    val = last_size + new_size;
+    last_size = new_size;
+    last_val = val;
+    (*x)[num_x] = val;
+    num_x += 1;
+    if (num_x == size){
+      size += 10;
+      *x = realloc(*x, size * sizeof(double));
+    }
+  }
+  
+  if (*y == NULL){
+    *y = malloc(num_x * sizeof(double));
+  }
+  else{
+    *y = realloc(*y, num_x * sizeof(double));
+  }
+  for (i=0; i < num_x; i++){
+    (*y)[i] = 0;
+  }
+
+  
+
+  for(i=0; i <N; i ++){
+    j = 0;
+    while(v[i] > (*x)[j]){
+      j ++;
+    }
+    (*y)[j] += 1;
+  }
+  *num = num_x;
+}
+
+/**
+ *
+ * Make the exponential binning of a distribution, with a giving
+ * exponent alpha. The value of y[i] is the average of the values in
+ * the vector "w" whose corresponding v lies between x[i-1] and  x[i]...
+ *
+ */
+
+
+void exp_bin_avg(double *v, double *w, int N, double alpha, double **x, double **y, int *num){
+  
+  double min_v, max_v, val, last_val;
+  int i, j, size, num_x;
+  double last_size, new_size;
+  int *cnt;
+
+
+  min_v = max_v = v[0];
+  
+  for (i=1; i<N; i ++){
+    if (v[i] > max_v)
+      max_v = v[i];
+    else if (v[i] > 0 && v[i] < min_v)
+      min_v = v[i];
+  }
+
+  size = 10;
+  if (*x == NULL){
+    *x = malloc(size * sizeof(double));
+  }
+  else{
+    *x = realloc(*x, size * sizeof(double));
+  }
+  
+  val = min_v;
+  last_size = min_v;
+  (*x)[0] = min_v;
+  num_x = 1;
+
+  while(val < max_v){
+    new_size = last_size * alpha;
+    val = last_size + new_size;
+    last_size = new_size;
+    last_val = val;
+    (*x)[num_x] = val;
+    num_x += 1;
+    if (num_x == size){
+      size += 10;
+      *x = realloc(*x, size * sizeof(double));
+    }
+  }
+  
+  
+  cnt = malloc(num_x * sizeof(int));
+  
+  if (*y == NULL){
+    *y = malloc(num_x * sizeof(double));
+  }
+  else{
+    *y = realloc(*y, num_x * sizeof(double));
+  }
+  for (i=0; i < num_x; i++){
+    (*y)[i] = 0;
+    cnt[i] = 0;
+  }
+
+  for(i=0; i <N; i ++){
+    j = 0;
+    while(j < num_x && v[i] > (*x)[j]){
+      j ++;
+    }
+    if(j == num_x){
+      printf("Error!!!!! Trying to assing a non-existing bin!!! -- fit_utils.c:exp_bin_avg!!!\n");
+      exit(37);
+    }
+    (*y)[j] += w[i];
+    cnt[j] += 1;
+  }
+  *num = num_x;
+  
+  for(i=0; i< num_x; i++){
+    if (cnt[i] > 0){
+      (*y)[i] = (*y)[i] / cnt[i];
+    }
+  }
+  free(cnt);
+}
+
+
+/**
+ *
+ * Print a distribution on stdout
+ *
+ */
+
+void dump_distr(double *x, double *y, int N){
+  int i;
+  
+  for(i=0; i<N; i ++){
+    printf("%g %g\n", x[i], y[i]);
+  }
+  
+}
+
+
+/**
+ * Compact a distribution, leaving only the pairs (x_i, y_i) for which
+ * y_i > 0
+ *
+ */
+
+void compact_distr(double *x, double *y, int *num){
+  
+  int i, j;
+  
+  i = j = 0;
+  while(j < *num){
+    while(j < *num && y[j] == 0){
+      j ++;
+    }
+    if (j==*num){
+      break;
+    }
+    x[i] = x[j];
+    y[i] = y[j];
+    i ++;
+    j ++;
+  }
+  *num = i;
+}
+
+
+/**
+ *
+ * Apply the function "f" on all the elemnts of a vector, in-place
+ *
+ */
+
+void map_vec(double *v, int N, double (*f)(double)){
+  int i;
+  
+  for (i=0; i<N; i ++){
+    v[i] = f(v[i]);
+  }
+}
+
+
+/**
+ *
+ * Normalize a distribution, dividing each y[i] for the width of the
+ * corresponding bin (i.e., x[i] - x[i-1])
+ *
+ */
+void normalize_distr(double *x, double *y, int num){
+  
+  int i;
+  
+  for(i=1; i<num; i ++){
+    y[i] /= (x[i] - x[i-1]);
+  }
+}
+
+/**
+ *
+ * take two vectors (k and q) and a pairing, and compute the best
+ * power-law fit "a*k^{mu}" of qnn(k)
+ *
+ */
+
+void fit_current_trend(double *k, double *q, int N, int *pairing, double *mu, double *a, 
+                       double *corr){
+
+  static int  *num;
+  static double *q_pair, *x, *y;
+
+  int i;
+  int fit_num;
+  double c0, c1, cov00, cov01, cov11, sqsum;
+  
+  if (q_pair == NULL){
+    q_pair = malloc(N * sizeof(double));
+  }
+
+  for(i=0; i<N; i++){
+    q_pair[i] = q[pairing[i]];
+  }
+
+  exp_bin_avg(k, q_pair, N, 1.3, &x, &y, &fit_num);
+  //normalize_distr(x,y, fit_num);
+  compact_distr(x, y, &fit_num);
+  
+  map_vec(x, fit_num, log);
+  map_vec(y, fit_num, log);
+  gsl_fit_linear(x, 1, y, 1, fit_num, &c0, &c1, &cov00, &cov01, &cov11, &sqsum);
+
+  //fprintf(stderr,"cov00: %g cov01: %g cov11: %g\n", cov00, cov01, cov11);
+  //fprintf(stderr, "corr: %g ", cov01 / sqrt(cov00 * cov11));
+  *a = c0;
+  *mu = c1;
+  *corr = cov01/sqrt(cov00 * cov11);
+}
+
-- 
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